• Registered: 2014-08-07
  • Posts: 40

Topic: Enigma?

Why this formula ...
Form1.EditA.Value := Round(2*Form1.EditAB.Value/(1+sqrt(5))) ;
give good result, and this result is different formula ...
Form1.EditA.Value := Round(Form1.EditAB.Value/((1+sqrt(5)/2))) ;
  because the mathematical point of view is the same

  • Registered: 2014-02-14
  • Posts: 10,294

Re: Enigma?

I think you wrong, it's not the same.


Try type it to google for check:

2*5/(1+sqrt(5))
5/((1+sqrt(5)/2))

Dmitry.
  • Registered: 2014-06-25
  • Posts: 863

Re: Enigma?

When doing the calculation by hand, it is not equal... smile

2*5/(1+sqrt(5)) = 10/(1+2,24) = 10/3,24 = 3,09


5/((1+sqrt(5)/2)) = 5/(1+2,24/2) = 5/2,12 = 2,36

It is a matter of parenthesis smile

5/((1+sqrt(5))/2) = 5/(3,24/2) = 5/1,62 = 3,09


Results are rounded.

4 Reply by einsteinf5 (edited by einsteinf5 2015-07-21 11:22:45)

  • Registered: 2014-08-07
  • Posts: 40

Re: Enigma?

I do not know how to do it but I think you're right tcoton, it was analyzed in more detail in parentheses am ..
it's ((1 + sqrt (5)) / 2)) = 1.61803398874989484820 Fibonacci's golden proportion, thanks for help
can help me make a script which automatically generate Fibonacci's sequence
where F (n) = F (n-1) + F (n-2) , n>2
Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987

phi = F (n + 1) / F (n) = ((1 + sqrt (5)) / 2)) = Golden Ratio = 1.61803398874989484820